In a right-angled triangle, one of the sharp corners is 25 degrees larger than the other.

In a right-angled triangle, one of the sharp corners is 25 degrees larger than the other. What are the acute angles of this triangle?

A right-angled triangle is a triangle with one of its angles equal to 90 °.
The triangle sum theorem states that the sum of all interior angles of any triangle is 180 °. Based on this theorem, the sum of the acute angles of a right-angled triangle is 180 ° – 90 ° = 90 °.
Let’s designate the smaller of the sharp angles as x, then the larger angle will be equal to 25 ° + x. Hence:
x + 25 ° + x = 90 °;
2 * x = 90 ° – 25 °;
2 * x = 65 °;
x = 65 ° / 2;
x = 32.5 °.
Thus, the smaller of the acute angles of a right-angled triangle is 32.5 °.
Then the degree measure of the larger acute angle is 25 ° + 32.5 ° = 57.5 °.
Answer: 32.5 ° and 57.5 °.